1. Technical Field
The present invention relates to an apparatus for generating long-period gratings in an optical fiber. More particularly, the present invention relates to an apparatus for generating the various periods of long-period gratings in a given arbitrary multi-mode optical fiber to couple two modes of various natural modes that can be present in the optical fiber.
2. Description of the Related Art
An optical fiber guides light based on the principle of total reflection attributable to the difference between the refractive indices of a core and a cladding. In this case, electric fields inside an optical fiber in a cross-sectional direction are present in a segmented form in a way that satisfies boundary conditions between a core, a cladding, and the outside of the optical fiber. These are referred to as optical fiber modes. Arbitrary light present in an optical fiber can be expressed by the linear coupling of the modes.
FIG. 1 illustrates the types of optical fiber modes that are linearly polarized. Optical fiber modes are classified as a mode (an LP0m) having no electric field node in an azimuthal direction and a mode (an LPlm mode; I>0) having an electric field node in an azimuthal direction. The LP0m mode is a symmetric mode, and the LPIm mode is an asymmetric mode.
The number of modes that can be present in an optical fiber may vary depending on parameters, such as the wavelength of propagating light, the difference between the refractive indices of a core and a cladding, and the size of the core. An optical fiber having a single optical fiber mode that can be present is referred to as a single-mode optical fiber at a predetermined wavelength, whereas an optical fiber having two or more modes that can be present is referred to as a few-mode optical fiber. Even the same optical fiber may have a different number of modes when a wavelength used in an optical fiber varies.
As is known to those skilled in the art, the propagation constant βlm in the LPlm mode is defined as 2πneff/λ, where λ is the wavelength and neff is the effective refractive index.
Each of the modes undergoes a phase change corresponding to a value obtained by multiplying the propagation constant of the mode by the propagation length thereof while propagating though an optical fiber. On the assumption that two different modes A and B propagate through an optical fiber, the relative phase difference between the two modes is periodically repeated from 0 to 2π, and the length over which a relative phase of modes is changed by 2π and returns to an original phase difference is referred to as a beat length LB. The beat length LB is calculated as follows:LB=(2π)/(βA−βB)
Meanwhile, examples of gratings generated in an optical fiber include, for example, Bragg gratings and long-period gratings. In Bragg gratings, when light having a wide bandwidth propagates through an optical fiber, the light is located at the center of a Bragg wavelength, a signal in a narrow bandwidth is reflected, and a signal in a band from which a Bragg wavelength has been removed is transmitted.
Long-period optical fiber gratings having a period ranging from 100 to 1000 μm (1 mm) are obtained by applying a periodic perturbation to the refractive index of a given optical fiber. Methods of applying a perturbation include mechanical minute bending, minute bending via sonic waves, a change in refractive index via an electric arc, and a change in refractive index via UV light.
The generation of gratings in an optical fiber is disclosed in the following documents.
U.S. Pat. No. 6,498,877 discloses a tunable optical fiber including gratings applied to at least a portion of a core. Tunability depends on an outermost layer which is applied to the outer layer of a cladding and whose refractive index is varied by a manipulation mechanism. That is, when the refractive index of the outermost layer is changed, the propagation constant of a cladding mode is also changed due to a change in the boundary condition, and the propagation constant of a core mode is also changed according to the distance from the boundary surface between the core and the cladding to the outermost layer.
Korean Patent No. 10-0274075 discloses a method of selectively converting the core mode of light, propagating through an optical fiber, into a cladding mode depending upon the wavelength of light using an elastic wave generator capable of varying the amplitude and wavelength of elastic waves through the control of the frequency and amplitude of an input electrical signal.
The paper of Estudillo-Ayala et al. discloses the principle of long-period fiber gratings, a production method using arc discharge, modulation using refractive indices, periodical modulation using minute taper or minute bending, the application fields of long-period fiber gratings, and a sensor (see Long Period Fiber Grating Produced by Arc Discharges, Julian M. Estudillo-Ayala et al., Universidad de Guanajuato, pp. 295-316, www.intechopen.com).
The paper of Hwang discloses a technology for linearly and tightly maintaining an optical fiber between two fiber holders, moving one of the fiber holders in a direction perpendicular to the axis of the optical fiber, for example, at intervals of 100 μm to thus generate lateral stress, and deforming a fiber by applying an electric arc to thus impart minute bends at regular intervals, preferably intervals of less than 1 μm (see Long-period fiber gratings based on periodic microbends, In Kag Hwang et al., Department of Physics, Korea advanced Institute of Science and Technology, Sep. 15, 1999/Vol. 24, No. 18/OPTICAL LETTERS pp. 1263-1265).
However, the above-described conventional technologies disclosed in the above documents have a limitation in that, when a pair of modes that will be coupled to each other are determined in an optical fiber and gratings are applied, this cannot be changed.
Accordingly, there is a need for an apparatus that is capable of overcoming the above problem, achieving the conversion between modes with minimum loss at the same time, and adjusting the interval and intensity of long-period gratings applied to an optical fiber.
First, the mode coupling theory is described as a background theory for long-period optical fiber gratings, as follows.
A Maxwell equation that should be satisfied by electric fields in an optical fiber in which an arbitrary perturbation has been applied to the refractive index of the core of the optical fiber is given as follows:
                    ▽        2            ⁢              E        ⁡                  (                      x            ,            y            ,            z                    )                      +                            ω          2                          c          2                    ⁢              {                              n            2                    +                      2            ⁢            n            ⁢                                                  ⁢            Δ            ⁢                                                  ⁢                          n              ⁡                              (                                  x                  ,                  y                  ,                  z                                )                                                    }            ⁢              E        ⁡                  (                      x            ,            y            ,            z                    )                      =  0where Δn(x, y, z) is a function that describes the perturbation of the refractive index.
Electric fields in an optical fiber system having a perturbation in refractive index can be expressed by the linear coupling of ideal step index optical fiber modes having no perturbation, that is, modes in which the refractive index changes from a core to a cladding in a stepped manner, as follows:
      E    ⁡          (              x        ,        y        ,        z            )        =            ∑              k        =                  -          ∞                    ∞        ⁢                            A          k                ⁡                  (          z          )                    ⁢                        F          k                ⁡                  (                      x            ,            y                    )                    ⁢              exp        ⁡                  (                      ⅈ            ⁢                                                  ⁢                          β              k                        ⁢            z                    )                    where z is the propagation direction of an optical fiber mode, Ak(z) is a intensity function according to the propagation direction of a k-mode, Fk(x, y) is a k-mode function in an ideal step index optical fiber having no perturbation, and βk is the propagation constant of the k-mode.
The following results are obtained by considering Ak(z) of the above equation to be a constant in the case of a propagation length of about one wavelength, adding a condition that the orthogonality of the mode Fk(x, y) and the perturbation of the refractive index are sinusoidal, and then substituting the condition into the Maxwell equation. The above condition is a condition that can be applied to the apparatus according to the present invention.
                    ∂        As                    ∂        z              =                  ∑                  k          =                      -            ∞                          ∞            ⁢                                    ⅈO            k            s                    ⁡                      (                          x              ,              y                        )                          ⁢                              A            k                    ⁡                      (            z            )                          ⁢        exp        ⁢                                  ⁢                  ⅈ          ⁡                      (                                          β                k                            -                              β                s                            -                                                2                  ⁢                                                                          ⁢                  π                                Λ                                      )                          ⁢        z                                ⅈO        k        s            ⁡              (                  x          ,          y                )              =                            2          ⁢          n          ⁢                                          ⁢                      ω            2                                                c            2                    ⁢          2          ⁢                                          ⁢                      β            s                              ⁢              ∫                              ∫                          -              ∞                        ∞                    ⁢                      Δ            ⁢                                                  ⁢                          n              ⁡                              (                                  x                  ,                  y                                )                                      ⁢                          F              k                        ⁢                          F              s              *                        ⁢                          ⅆ              x                        ⁢                                                  ⁢                          ⅆ              y                                          
The following simultaneous differential equations are obtained by considering only two modes again.
                    ∂                  A          a                            ∂        z              =                  ⅈO        b        a            ⁢              A        b            ⁢      exp      ⁢                          ⁢              ⅈ        ⁡                  (                                    β              a                        -                          β              b                        -                                          2                ⁢                                                                  ⁢                π                            Λ                                )                    ⁢      z                          ∂                  A          b                            ∂        z              =                  ⅈO        a        b            ⁢              A        a            ⁢              expⅈ        ⁡                  (                                    β              b                        -                          β              a                        -                                          2                ⁢                                                                  ⁢                π                            Λ                                )                    ⁢      z      where Oba is simply expressed as O and is the coupling intensity constant between modes a and b, Oba is the conjugate complex number of Oba, and Λ is a perturbation period.
Finally, the intensity at which the initial mode a is coupled to the mode b can be expressed by the following Equation 1 by solving the simultaneous differential equations:
                                                                      o                                      2                                                                              o                                            2                        +                                          (                                  Δ                  ⁢                                                                          ⁢                                      β                    /                    2                                                  )                            2                                      ⁢                              sin            2                    ⁡                      [                                                                                                    o                                                        2                                +                                                      (                                          Δ                      ⁢                                                                                          ⁢                                              β                        /                        2                                                              )                                    2                                                      ]                                              (        1        )            where
      Δ    ⁢                  ⁢    β    =            β      a        -          β      b        -                  2        ⁢        π            Λ      represents non-phase matching, and o is the mode coupling constant.
The result of Equation 1 determines factors that should be considered in long period optical fiber gratings for the coupling of modes.
Although various methods of generating gratings in a long-period optical fiber are present, the present invention employs a method of applying minute bending by mechanically pressing an optical fiber. When minute bending is applied to an optical fiber, the partial stress attributable to the curvature of the optical fiber generates a perturbation Δn(x, y) in refractive index that is asymmetrical with respect to the x-y direction in the core portion of the optical fiber.
Furthermore, in order to achieve a 100% coupling from one mode to another mode, the non-phase matching Δβ should be zero. This can be achieved when the period of applied gratings completely coincides with the beat length of two modes that will be coupled to each other.
Referring to Equation 1, the coupling of modes can be achieved only when the mode coupling intensity constant is not zero. Since the perturbation in refractive index generated in a minute bending manner is asymmetrical with respect to the x-y direction, the coupling between a symmetrical mode and an asymmetrical mode can be achieved. If the two modes that will be coupled to each other are a symmetric mode and an asymmetric mode, the coupling intensity constant can be adjusted through the intensity of mechanical pressure that is used to generate minute bending.